Jeromie,
Thanks for your assistance. Sorry to take so long to report on things, but wanted to try out what you suggested and hopefully resolve the issue.
After disabling all my Add-Ons (Safe Mode), the Insufficient Message still appeared when attempting to view live streaming on the website in question. Incidentally, I got a similar message on a completely different siteScout's Inside Tennessee websitewhere a message said, "html5: Unsupported video format. Try installing Adobe Flash." I could provide you the link, but without a paid subscription to the service, you wouldn't be able to pull it up.
I then individually disabled all my plug-ins (except Flash) by making them Never Activate. Unbelievably, the Insufficient message continued to display. One question: must one close Foxfire each time he disables something or does it respond immediately to the actions on the Add-On and Plug-In pages? I did not do that, but each time I tested something I first did hit the Refresh button; each time, the Insufficient message immediately appeared even before an index or anything else appeared.
This mystifies me; it's almost like when a person's hand gets cut off, and he can still feel a "phantom" limb. I had hoped to be able to close this case, but...do you have any other possibilities?
Regards,
David
Okay, I had to re-read the thread, but you're good on Chrome, so this sounds like just a Firefox thing at this point. We've eliminated plug-ins from the equation, so now we're just left with the ugly possibilities. 
My guess is that something is screwy with the filesystem or the Windows registry and while our installer is successful, it's not getting registered with Firefox as a valid plug-in.
Here's what I'd do:
If you have anything important on the machine, make sure you have a current working backup before starting.
Make sure that the filesystem is in a good state:
How to perform disk error checking in Windows XP
Delete any installers that you might have in your downloads folder or desktop.
Uninstall both Flash Player and Firefox
Uninstalling Firefox - MozillaZine Knowledge Base
How do I do a clean install of Flash Player?
Reboot
Download and install a fresh copy of Firefox from here:
Download Firefox — Free Web Browser — Mozilla
Download and install Flash Player for Firefox and other NPAPI browsers:
http://fpdownload.macromedia.com/pub/flashplayer/latest/help/install_flash_player.exe
Hopefully that gets you going.